The algebraic approach for the derivation of ladder operators and coherent states for the Goldman and Krivchenkov oscillator by the use of supersymmetric quantum mechanics

Abstract

The ladder operators for the Goldman and Krivchenkov anharmonic potential have been derived within the algebraic approach. The method is extended to include the rotating oscillator. The coherent states for the Goldman and Krivchenkov oscillator, which are the eigenstates of the annihilation operator and minimize the generalized position-momentum uncertainty relation, are constructed within the framework of supersymmetric quantum mechanics. The constructed ladder operators can be a useful tool in quantum chemistry computations of non-trivial matrix elements. In particular, they can be employed in molecular vibrational-rotational spectroscopy of diatomic molecules to compute transition energies and dipole matrix elements.

One-dimensional pseudoharmonic oscillator: classical remarks and quantum-information theory

“…Let us note that position (wave vector) component is measured in the units of length (inverse length) what makes equation (33) the most symmetric (and, accordingly, advantageous) compared to the use of the momentum p = ÿk instead of k. For PHO, the position mean value reads:…”

“…was first introduced (with the simplifying assumption 1 a = ) more than sixty years ago in a problem-solving textbook on quantum mechanics [16]. Despite of a such venerable age [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34], some properties of the movement in the similar type potentials that are commonly referred to as pseudoharmonic oscillator (PHO) still have not been addressed; namely, whereas quantum information measures, such as Shannon [35,36], Rényi [37,38] and Tsallis [39] entropies, Fisher information [40,41], Onicescu energy [42], have recently been calculated for the 2D [14,15] and 3D [4] PHO, their 1D counterparts still almost have not been tackled with: the only exception is the discussion of the position and momentum Shannon and position Fisher functionals for the half harmonic oscillator (HHO) [43], i.e., the structure with 0 a = . The primary aim of the present exposition is to close this gap.…”

Ladder operators and coherent states for the Rosen–Morse system and its rational extensions

“…The use of the number operator in the construction of A ± arise from the fact that the operators needs to vary depending on the excitation of the state it acts on. Standard construction techniques can be found in [3,[23][24][25]. However, in this work we consider the Rosen-Morse system, for which a first order realization such as ( 7) cannot be achieved using standard methods [14].…”

Ladder operators and coherent states for the Rosen-Morse system and its rational extensions

“…The use of the number operator in the construction of A ± arise from the fact that the operators needs to vary depending on the excitation of the state it acts on. Standard construction techniques can be found in [3,22,23,24]. However, in this work we consider the Rosen-Morse system, for which a first order realization such as (7) cannot be achieved using standard methods [14].…”